Question

kuta software - infinite geometry
the segment addition postulate
find the length indicated.

1. ( h \bullet quad ? quad \bullet g \bullet f ) (with ( gf = 1 ), blue arrow from ( h ) to ( g ) (or ( h ) to ( f )) labeled ( 10 ))

Explanation:

Step1: Apply Segment Addition Postulate

The Segment Addition Postulate states that if \( G \) is between \( H \) and \( F \), then \( HF = HG + GF \). We know \( HF = 10 \) and \( GF = 1 \), so we can solve for \( HG \).
\[ HG + GF = HF \]
\[ HG + 1 = 10 \]

Step2: Solve for \( HG \)

Subtract 1 from both sides of the equation.
\[ HG = 10 - 1 \]
\[ HG = 9 \]

Answer:

9